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PEAMCQModerate

2025 PEA Q22

Two demand groups. Both stop at p=5p = 5. Per Re.\ price decrease: student demand +5+5, professor demand +10+10. MC=1MC = 1. Who is charged more?

Reveal answer and solution

Answer

C

Solution

  1. 1

    Student demand: QS=5(5−p)Q_S = 5(5-p) for p≤5p\le 5, i.e.\ p=5−QS/5p = 5 - Q_S/5.

  2. 2

    Professor demand: QP=10(5−p)Q_P = 10(5-p), i.e.\ p=5−QP/10p = 5 - Q_P/10.

  3. 3

    Marginal revenues:

  4. 4
    MRS=5−2QS5,MRP=5−QP5. MR_S = 5 - \tfrac{2Q_S}{5},\qquad MR_P = 5 - \tfrac{Q_P}{5}.
  5. 5

    Set MR=MC=1MR = MC = 1:

  6. 6
    QS∗=10,pS∗=5−2=3. Q_S^* = 10,\quad p_S^* = 5 - 2 = 3.
  7. 7
    QP∗=20,pP∗=5−2=3. Q_P^* = 20,\quad p_P^* = 5 - 2 = 3.
  8. 8

    Both groups face p=3p = 3.

Answer structure / marking notes

With the same choke price (p=5p=5) and same MC, only the slope changes; the optimal price is identical (the monopolist halves the gap between choke price and MC).

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Content note

Imported from public/resources/isi/msqe/solutions/pea/2025/ISI_MSQE_PEA_2025_Solutions.tex. Question wording is retained from the available local TeX source; incomplete option blocks or ambiguous source status are flagged for review.